﻿#region License

// Copyright 2007-2008 Rory Plaire (codekaizen@gmail.com)
/*
 * This license governs use of the accompanying software. If you use the software, you
 * accept this license. If you do not accept the license, do not use the software.
 *
 * 1. Definitions
 * The terms "reproduce," "reproduction," "derivative works," and "distribution" have the
 * same meaning here as under U.S. copyright law.
 * A "contribution" is the original software, or any additions or changes to the software.
 * A "contributor" is any person that distributes its contribution under this license.
 * "Licensed patents" are a contributor's patent claims that read directly on its contribution.
 *
 * 2. Grant of Rights
 * (A) Copyright Grant- Subject to the terms of this license, including the license conditions
 *     and limitations in section 3, each contributor grants you a non-exclusive, worldwide,
 *     royalty-free copyright license to reproduce its contribution, prepare derivative works
 *     of its contribution, and distribute its contribution or any derivative works that you create.
 * (B) Patent Grant- Subject to the terms of this license, including the license conditions and
 *     limitations in section 3, each contributor grants you a non-exclusive, worldwide, royalty-free
 *     license under its licensed patents to make, have made, use, sell, offer for sale, import,
 *     and/or otherwise dispose of its contribution in the software or derivative works of the
 *     contribution in the software.
 *
 * 3. Conditions and Limitations
 * (A) No Trademark License- This license does not grant you rights to use any contributors'
 *     name, logo, or trademarks.
 * (B) If you bring a patent claim against any contributor over patents that you claim are
 *     infringed by the software, your patent license from such contributor to the software
 *     ends automatically.
 * (C) If you distribute any portion of the software, you must retain all copyright, patent,
 *     trademark, and attribution notices that are present in the software.
 * (D) If you distribute any portion of the software in source code form, you may do so only under
 *     this license by including a complete copy of this license with your distribution. If you
 *     distribute any portion of the software in compiled or object code form, you may only do so
 *     under a license that complies with this license.
 * (E) The software is licensed "as-is." You bear the risk of using it. The contributors give no
 *     express warranties, guarantees or conditions. You may have additional consumer rights under
 *     your local laws which this license cannot change. To the extent permitted under your local laws,
 *     the contributors exclude the implied warranties of merchantability, fitness for a particular
 *     purpose and non-infringement.
 *
 */

#endregion License

using System;

namespace NPack.Interfaces
{
    /// <summary>
    /// Cholesky Decomposition
    /// <para/>
    /// For a symmetric, positive definite matrix A, the Cholesky decomposition
    /// is an lower triangular matrix L so that A = L*L'.
    /// <para/>
    /// If the matrix is not symmetric or positive definite, the constructor
    /// returns a partial decomposition and sets internal flags that may
    /// be queried by the <see cref="PositiveDefinite"/> and <see cref="Symmetric"/> property.
    /// </summary>
    /// <typeparam name="TComponent">The type of the matrix components</typeparam>
    /// <typeparam name="TMatrix">The type of the matrix</typeparam>
    public interface ICholeskyDecomposition<TComponent, TMatrix> : IFactorization<TComponent, TMatrix>
        where TComponent : struct, IEquatable<TComponent>, IComparable<TComponent>, IComputable<TComponent>, IConvertible
        where TMatrix : IMatrix<TComponent, TMatrix>, IEquatable<TMatrix>, IComparable<TMatrix>, IComputable<TMatrix>
    {
        /// <summary>
        /// Gets the left triangular factor
        /// </summary>
        TMatrix LeftTriangularFactor { get; }

        /// <summary>
        /// Gets whether the matrix symmetric and positive definite
        /// </summary>
        Boolean PositiveDefinite { get; }

        /// <summary>
        /// Solve A*X = B
        /// </summary>
        /// <param name="matrixB">A <typeparamref name="TMatrix"/> with as many rows as A and any number of columns.</param>
        /// <returns>X so that L*L'*X = B</returns>
        /// <exception cref="ArgumentException">Matrix row dimensions must agree.</exception>
        /// <exception cref="InvalidOperationException">Matrix is not symmetric positive definite.</exception>
        TMatrix Solve(TMatrix matrixB);

        /// <summary>
        /// Gets whether the L matrix is symmetric
        /// </summary>
        Boolean Symmetric { get; }
    }
}